Is the husband's statement to his mother, "If you want me to divorce my wife, I will do so," considered a conditional divorce, and what is the ruling if the mother agrees to the request?

Your statement to your mother: "If you want me to divorce my wife, I will do so," is not a suspension of divorce, but rather a promise of it. Therefore, divorce does not occur with this phrase, whether your mother wants you to divorce your wife or not; because a promise of divorce does not result in divorce, and there is no obligation to fulfill it, as explained by Sheikh al-Islam Ibn Taymiyyah.